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V.2 Compare decimals using place value grids

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What does it mean to compare decimals?

Comparing decimals means deciding which number is greater, less, or if they are equal. We use the digits and their place values to make this comparison.

Example:
  • 0.6 is greater than 0.54 because 6 tenths is more than 5 tenths.
  • 0.35 is less than 0.4 because 3 tenths is less than 4 tenths.
Note

Always line up the decimal points before comparing. This helps you see which digits are in the same place value positions.

Using a place value grid to compare decimals

A place value grid helps you organize digits by their place values—ones, tenths, hundredths, and so on. It shows how much each digit is worth.

Example:

Compare 0.47 and 0.5 using a place value grid:

  • 0.47 has 4 tenths and 7 hundredths.
  • 0.5 has 5 tenths and 0 hundredths.
  • Since 5 tenths is greater than 4 tenths, 0.5 is greater than 0.47.
Note

If one decimal stops sooner, you can add a zero to the end without changing its value. For example, 0.5 = 0.50.

Steps to compare decimals

Follow these steps to compare decimals accurately using place value understanding.

Steps:
  • 1. Line up the decimal points.
  • 2. Compare the digits from left to right (ones, tenths, hundredths, etc.).
  • 3. The first place where the digits differ decides which number is greater.
  • 4. Use the symbols <, >, or = to show the comparison.
Note

Remember: The farther left a digit is, the greater its value. Always start comparing from the highest place value.

Example comparisons

Here are some examples showing how to compare decimals correctly using place value reasoning.

Examples:
  • 0.72 > 0.65 (7 tenths is greater than 6 tenths)
  • 1.03 < 1.3 (1 tenth is greater than 0 tenths)
  • 0.45 = 0.450 (adding a zero does not change the value)
Note

Always read decimals carefully—zeros after the last nonzero digit do not change the number’s value.

Check your understanding

When you compare decimals, ask yourself: Which digit shows the greater value in the first place where they differ?

Example Question:

Which is greater: 0.68 or 0.7?

  • Line up the decimals: 0.68 and 0.70
  • Compare tenths: both have 6 and 7 tenths → 7 tenths is greater.
  • Therefore, 0.7 > 0.68.
Note

If you compare decimals correctly, you can also order them from least to greatest or greatest to least with confidence.

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